I removed the default borders in the main step:
stage.initStyle(StageStyle.UNDECORATED)
This removes the window borders that I want, but now I want to have a shadow under the window.
The top-level object BorderPanehas an effect dropshadow, but the shadow is disabled:

You can slightly see the shadow in the lower right corner, but as soon as the main application area ends, the shadow turns off.
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